Question

which expression is equivalent to $9 + 4 \cdot 16$
a) $3^2 + 2^3 \cdot 8$
b) $3^2 \cdot 2^3 + 3^2$
c) $3^3 + 2^4 \cdot 4$
d) $3^3 + 2^2 \cdot 3^2$

Explanation:

Step1: Calculate original expression

First, apply order of operations (multiplication before addition):
$9 + 4 \cdot 16 = 9 + 64 = 73$

Step2: Evaluate option a)

Calculate exponents, then multiplication, then addition:
$3^2 + 2^3 \cdot 8 = 9 + 8 \cdot 8 = 9 + 64 = 73$

Step3: Evaluate option b)

Calculate exponents, multiplication, then addition:
$3^2 \cdot 2^3 + 3^2 = 9 \cdot 8 + 9 = 72 + 9 = 81$

Step4: Evaluate option c)

Calculate exponents, multiplication, then addition:
$3^3 + 2^4 \cdot 4 = 27 + 16 \cdot 4 = 27 + 64 = 91$

Step5: Evaluate option d)

Calculate exponents, multiplication, then addition:
$3^3 + 2^2 \cdot 3^2 = 27 + 4 \cdot 9 = 27 + 36 = 63$

Answer:

a) $3^2 + 2^3 \cdot 8$